Math Problem Statement

Solve the following system of equations graphically on the set of axes below. y, equals, x, plus, 6 y=x+6 y, equals, minus, start fraction, 3, divided by, 2, end fraction, x, minus, 4 y=− 2 3 ​ x−4 can you draw the plot points

Solution

Here is the graphical representation of the system of equations:

  1. y=x+6y = x + 6 (in blue)
  2. y=−32x−4y = -\frac{3}{2}x - 4 (in red)

The point where these two lines intersect represents the solution to the system of equations. From the graph, you can identify the point of intersection, which will give the solution to the system.

Would you like me to calculate the exact point of intersection or provide more details?

Here are some related questions to expand on this:

  1. What is the algebraic method for solving a system of linear equations?
  2. How do you find the intersection point algebraically?
  3. Can you graph a system of equations with non-linear terms?
  4. How does the slope of a line affect the solution of a system of equations?
  5. How would you solve this system if both equations were quadratic?

Tip: The slope of a line represents how steep the line is; in the equation y=mx+by = mx + b, the slope is mm, and it plays a key role in determining how lines interact (parallel, intersect, or overlap).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing Systems of Equations

Formulas

y = mx + b (Slope-intercept form of a linear equation)
Intersection of two lines

Theorems

Slope-Intercept Theorem
Intersection Point Theorem

Suitable Grade Level

Grades 8-10

Related Recommendation

Solving Systems of Linear Equations Graphically: y = x + 6 and y = −(3/2)x − 4

Graphing Linear Equations: y = x + 6 and y = -(3/2)x - 4

Solve System of Equations by Graphing: y = -1/2x - 6 and y = -3x + 4

Solving System of Linear Equations Graphically: y = x + 3 and y = -1/2x - 6

Solve the System of Equations: y = -2x and y = (4/3)x